In manufacturing advanced device products such as a hard disk drive unit, an integrated circuit and a liquid crystal display, the fineness of the products and the complexity of a manufacturing process are remarkable, whereby it becomes difficult to manufacture the products according to the design drawing. Some of the products may become defective due to variations in various kinds of parameters in the manufacturing process. The manufacturing maker makes an effort to improve the yield by decreasing the defective products occurring in the manufacturing process as much as possible to reduce the manufacturing costs.
Therefore, it is required to analyze various kinds of parameters acquired in manufacturing the products, rapidly find a parameter that causes failure occurrence, and take measures for preventing the parameter from being varied. Particularly, if the measures can be taken in order from the parameter having the most influence on the lower yield, the products can be produced in a state where the yield is as high as possible, greatly contributing to the business.
The following techniques concerning the conventional data analysis method used to find out the parameter becoming causes of failure occurrence are well known.
For example, in patent document 1 (Japanese Laid-Open Patent No. A-9-27531), patent document 2 (Japanese Laid-Open Patent No. A-2003-186953) and patent document 3 (Japanese Laid-Open Patent No. A-2001-110867, a method for performing a simple regression analysis for the data group was disclosed in which the yield is taken along the vertical axis and each parameter is taken along the horizontal axis. However, the simple regression analysis presupposes that the data group conforms to a normal distribution, and is not appropriately applied to the data group not conforming to the normal distribution.
Also, a logistic regression analysis may be effectively employed to compute the data group indicating the ratio such as yield which is taken along the vertical axis, as described in non-patent document 1 (Tango, Yamaoka, Takagi: Logistic regression analysis, Asakura Shoten (1996)) and non-patent document 2 (Hirono: Applied logistic regression analysis—Introduction of application examples to quality control, Japan SAS user society treatise (SUGI-J), pp. 203-208 (1992)). Thus, it is considered that the logistic regression analysis is applied to the data group actually obtained at the time of manufacture, but while the contradictory result that as the number of defects increases the yield becomes better is true in some cases, it is not said that this logistic regression analysis is necessarily favorable.
Also, there is a method for classifying beforehand the data group obtained during the manufacture into the first group and the second group, based on the test results of the performance or yield of the products, and calculating the significant probability of the data group belonging to the first group and the data group belonging to the second group employing the T test or the analysis of variance (ANOVA) for each parameter, as described in patent document 3 and non-patent document 3 (Tanaka, Tarumi: Statistical analysis handbook/non-parametric method, Kyoritsu shuppan (1999)).
However, this method, like the simple regression analysis, and also presupposes that the data group conforms to the normal distribution, and can not be appropriately applied to the data group not conforming to the normal distribution. Also, in the T test or the analysis of variance, the value acquired as a result of the analysis is the statistical quantity of the significant probability, whereby there is a problem that it is not possible to estimate how much the yield is increased by taking measures for the parameter of interest.
An analysis method is provided in which the individual values of data are not noted, but the order of data is noted by arranging the data group in order of size, as described in non-patent document 4 (Tanaka, Tarumi: Statistical analysis handbook/non-parametric method, Kyoritsu shuppan (1999)) and patent document 4 (U.S. Patent Publication No. 2005/0071103A1). This analysis method is generally called a non-parametric method. Various methods as described in non-patent document 4 calculate the significant probability, like the T test and the analysis of variance, and can not estimate how much the yield is increased by taking measures for the parameter of interest. On the other hand, a method for graphically representing how much the yield of the final products is increased when the data group is arranged and the parts are destroyed in the order from the larger or smaller data value was described in patent document 4. This method is effective for increasing the yield of the final products by providing the strict specification values of parts built into the final products, and destroying the parts. However, it is not possible to estimate how much the yield is increased by improving the manufacturing process without changing the specification values of the parts.
The above methods as described in the patent documents 1 to 3 and the non-patent documents 1 to 3 depend on the distribution of data group, and are insufficient to select the parameter having the most significant influence on the occurrence of a failure by comparing the parameters having the data groups with various distributions. Also, there is another problem in not knowing how much the yield is increased in taking measures for the selected parameter.
On the other hand, the non-parametric methods as described in the patent document 4 and the non-patent document 4 can solve the above problem regarding the distribution of data group because they do not depend on the distribution of data group. Particularly, the method as described in the patent document 4 can quantify how much the yield of the final products is increased with respect to the quantity of destroyed parts. However, it is not possible to estimate how much the yield is increased by improving the manufacturing process without increasing the quantity of destroyed parts, as described above.